Embodied Computing

1. Embodied Computing Bruce J. MacLennan Dept. of Electrical Engineering & Computer Science University of Tennessee, Knoxville

2. Outline • Recent Research • Molecular combinatory computing • Generalized computation & the U-machine • Artificial morphogenesis • New Directions • Convergence of scales • Novel characteristics • Need for new models of computation • Embodied computing NSF Workshop: Biological Communications Technology

3. formal material Central Themes • Computation and physics • novel computational models toexploit novel technologies • computational control of matter • Natural computation • computation occurring in nature, or • inspired by that occurring in nature NSF Workshop: Biological Communications Technology

4. Current Research inEmbodied Computing • Molecular Combinatory Computing • Generalized Computation • Artificial Morphogenesis NSF Workshop: Biological Communications Technology

5. Molecular Combinatory ComputingforNanostructure Synthesis & Control Supported by NSF Nanoscale Exploratory Research Grant NSF Workshop: Biological Communications Technology

6. Molecular Combinatory Computing • Systematic approach to nanotechnology based on small set of MBBs • Combinatory logic • Computational universality from two substitutions (+ a few more) • Substitutions may be done in any order or in parallel NSF Workshop: Biological Communications Technology

7. K-Substitution ((K X) Y)  X NSF Workshop: Biological Communications Technology

8. S-Substitutions (((SX) Y) Z)  ((X Z) (Y Z)) NSF Workshop: Biological Communications Technology

9. Ý-Substitution (ÝF) y(1) where y (F y(0)) NSF Workshop: Biological Communications Technology

10. Example of Simple Computation ((S(KS)K)S) (((KS)S)(KS)) NSF Workshop: Biological Communications Technology

11. Example of Simple Computation ((KS)S)  S NSF Workshop: Biological Communications Technology

12. Example of Simple Computation (((S(KS)K)K) (((KS)K)(KK)) NSF Workshop: Biological Communications Technology

13. Example of Simple Computation ((KS)K)  S NSF Workshop: Biological Communications Technology

14. Example of Simple Computation result = (S(KK)) NSF Workshop: Biological Communications Technology

15. Example: Nanotube Visualization of nanotube produced by ptube5,4 NSF Workshop: Biological Communications Technology

16. Example: Nanotube NSF Workshop: Biological Communications Technology

17. In Functional Programming Language let prib(m) = compose (polyextend shared-formalize m) rib where rib = polyextend compose m cycle (reduce permute m identity) in let ptube(m, n) = iterate n prib(m) in ptube(5, 4) NSF Workshop: Biological Communications Technology

18. Reduced to SKY Tree (((S ((S (K S)) K)) ((S ((S (K S)) K)) ((S ((S (K S)) K)) ((S ((S (K S)) K)) (K ((S K) K)))))) ((((S ((((S (K S)) K) ((S (K S)) K)) S)) (K K)) ((((S (K S)) K) S) (((S (K S)) K) ((((S (K S)) K) S) (((S (K S)) K) ((((S (K S)) K) S) (((S (K S)) K) ((((S (K S)) K) S) (((S (K S)) K) S))))))))) ((((((S (K S)) K) ((S (K S)) K)) ((((S (K S)) K) ((S (K S)) K)) ((((S (K S)) K) ((S (K S)) K)) ((((S (K S)) K) ((S (K S)) K)) ((S (K S)) K))))) Y) (((((S (K S)) K) (((S (K S)) K) ((((S (K S)) K) (((S (K S)) K) ((((S (K S)) K) (((S (K S)) K) ((((S (K S)) K) (((S (K S)) K) ((S ((((S (K S)) K) ((S (K S)) K)) S)) (K K)))) ((S ((((S (K S)) K) ((S (K S)) K)) S)) (K K))))) ((S ((((S (K S)) K) ((S (K S)) K)) S)) (K K))))) ((S ((((S (K S)) K) ((S (K S)) K)) S)) (K K))))) ((S ((((S (K S)) K) ((S (K S)) K)) S)) (K K))) ((S K) K))))) NSF Workshop: Biological Communications Technology

19. Linearized for Chemical Synthesis & Replication PPPS PPS PK SQQ KQQ PPS PPS PK SQQ KQQ PPS PPS PK SQQ KQQ PPS PPS PK SQQ KQQ PK PPS KQ KQQQQQQ PPPPS PPPPS PK SQQ KQ PPS PK SQQ KQQ SQQ PK KQQ PPPPS PK SQQ KQ SQ PPPS PK SQQ KQ PPPPS PK SQQ KQ SQ PPPS PK SQQ KQ PPPPS PK SQQ KQ SQ PPPS PK SQQ KQ PPPPS PK SQQ KQ SQ PPPS PK SQQ KQ SQQQQQQQQQ PPPPPPS PK SQQ KQ PPS PK SQQ KQQ PPPPS PK SQQ KQ PPS PK SQQ KQQ PPPPS PK SQQ KQ PPS PK SQQ KQQ PPPPS PK SQQ KQ PPS PK SQQ KQQ PPS PK SQQ KQQQQQ YQ PPPPPS PK SQQ KQ PPPS PK SQQ KQ PPPPS PK SQQ KQ PPPS PK SQQ KQ PPPPS PK SQQ KQ PPPS PK SQQ KQ PPPPS PK SQQ KQ PPPS PK SQQ KQ PPS PPPPS PK SQQ KQ PPS PK SQQ KQQ SQQ PK KQQQQ PPS PPPPS PK SQQ KQ PPS PK SQQ KQQ SQQ PK KQQQQQ PPS PPPPS PK SQQ KQ PPS PK SQQ KQQ SQQ PK KQQQQQ PPS PPPPS PK SQQ KQ PPS PK SQQ KQQ SQQ PK KQQQQQ PPS PPPPS PK SQQ KQ PPS PK SQQ KQQ SQQ PK KQQQ PPS KQ KQQQQQ NSF Workshop: Biological Communications Technology

20. Molecular Computation NSF Workshop: Biological Communications Technology

21. Hexagonal Membrane Produced by hgridt2,3N Arown = BW[n-1]B[n] Vrown = W[n]KIK(2n-2) B[n-1]C[n]INCIN drowtn = VrowtnArown hgridtm,n = Zn-1W(ZmdrowtnN) NSF Workshop: Biological Communications Technology

22. Possible Molecular Implementation • Covalently-structured MBBs for nodes and linking groups • H-bonds for interconnections • H-bonds for identification • Synthetic components appended • Substitutions controlled by enzyme-like covalently-structured molecules NSF Workshop: Biological Communications Technology

23. Progress to Date • Simulation & theoretical studies: • ways of assembling hierarchical heterogeneous structures from patches • membranes, pores, sensor interface, one-shot channels, simple actuators, nanotubes • In progress: • recyclable channels, cilia, rotary motion • molecular implementations (including DNA) NSF Workshop: Biological Communications Technology

24. Pros and Cons • Pros • universal • substitutions can be done in any order or in parallel • Cons • not fault- or error-tolerant • computational universality does not imply synthetic/behavioral universality • requires aqueous medium NSF Workshop: Biological Communications Technology

25. Summary of MCC • Concept of molecular combinatory computing • molecular networks self-organize by simple substitution reactions • computationally universal • Simulated synthesis applications • Synthesis of large, heterogeneous structures • Possible molecular implementation based on H-bonded, covalently-structured building blocks NSF Workshop: Biological Communications Technology

26. Generalized Computationand the U-Machine NSF Workshop: Biological Communications Technology

27. Computation in General Sense • A definition applicable to computation in nature as well as in computers • Computation is a physical process, the purpose of which is abstract operation on abstract objects • A computation must be implemented by some physical system, but it may be implemented by any physical system with the appropriate abstract structure NSF Workshop: Biological Communications Technology

28. Abstract Spaces • Should be general enough to include continuous & discrete spaces • Hypothesis: separable metric spaces • Include continua & countable discrete spaces • separable ⇒ approximating sequences NSF Workshop: Biological Communications Technology

29. The U-Machine • Goal: a model of computation over abstract spaces that can be implemented in a variety of physical media • In particular, bulk nanostructured materials in which: • access to interior is limited • detailed control of structure is difficult • structural defects and other imperfections are unavoidable NSF Workshop: Biological Communications Technology

30. Urysohn Embedding NSF Workshop: Biological Communications Technology

31.   U W V f g Computation in Hilbert Space NSF Workshop: Biological Communications Technology

32. Overall Structure • Variable (data) space • Large number of scalar variables for Hilbert coefficients • Partitioned into regions representing abstract spaces • Function (program) space • Flexible interconnection ( 3D) • Programmable linear combinations • Application of basis functions NSF Workshop: Biological Communications Technology

33. Depiction of UM Interior • Shell contains variable areas & computational elements • Interior filled with solid or liquid matrix (not shown) • Paths formed through or from matrix NSF Workshop: Biological Communications Technology

34. Layers in Data Space • Connection matrix has programmable weights • Linear combinations are inputs to nonlinear basis functions • Exterior access to both sides for programming NSF Workshop: Biological Communications Technology

35. Depiction of UM Exterior NSF Workshop: Biological Communications Technology

36. Diffusion-Based Path Routing NSF Workshop: Biological Communications Technology

37. Example of Path Routing • Starts and ends chosen randomly • Quiescent interval (for attractant decay) omitted from video • Each path occupies ~0.1% of space • Total: ~4% NSF Workshop: Biological Communications Technology

38. Front NSF Workshop: Biological Communications Technology

39. Remarks • More realistic procedure: • Systematic placement of regions • Order of path growth • Control of diffusion & growth phases • General approach is robust (many variations work about as well) • Paths could be formed by: • Migration of molecules etc. • Change of state of immobile molecules NSF Workshop: Biological Communications Technology

40. Example Connection-Growth Process • Goal: approximately full interconnection between incoming “axons” (A) and “dendrites” (D) of basis functions • Doesn’t have to be perfect • Each A & D periodically initiates fiber growth • Growth is approximately away from source • Fibers repel others of same kind • Diffusible, degradable repellant • Fibers follow decreasing gradient (in XZ plane) • Contact formed when A and D fibers meet NSF Workshop: Biological Communications Technology

41. Example of Connection Formation • 10 random “axons” (red) and “dendrites” (blue) • Simulation stopped after 100 connections (yellow) formed NSF Workshop: Biological Communications Technology

42. Resulting Connections NSF Workshop: Biological Communications Technology

43. Summary of U-Machine • Permits computation on quite general abstract spaces (separable metric spaces) • Includes analog & digital computation • Computation by linear combinations & simple nonlinear basis functions • Simple computational medium can be reconfigured for different computations • Potentially implementable in a variety of materials NSF Workshop: Biological Communications Technology

44. Programmable MicroorganismsforArtificial Morphogenesis

45. Artificial Morphogenesis • Based on models of embryological development • Cells migrate by local interaction & chemical signals • Possible implemen-tation: “programmable” micro-organisms • But there may be others NSF Workshop: Biological Communications Technology

46. Multiscale Assembly • Assembly from nanoscale to macroscale • Macroscopic test cases (“killer apps”?): • multilayer tissues • tubes • articulated structures • periodic structures • branching structures • bristles • somatic regions NSF Workshop: Biological Communications Technology

47. Cellular/atomic translation/rotation adhesion/release conformal change differentiation/state change collision/interaction apoptosis Continuum elasticity diffusion degradation fluid flow gradient ascent Some Primitives NSF Workshop: Biological Communications Technology

48. Programmed Morphogenesis • Libraries of operations • diffusion • degradation • gradient ascent • activation-inhibition • proliferation/apoptosis • elasticity • etc. • Coordinated algorithms NSF Workshop: Biological Communications Technology

49. Why Micro-Organisms? • Micro-organisms can be viewed a micro-robots with capabilities for: • locomotion • sensing • control • simple (low-precision analog) computation • assembly • collective, coordinated behavior • reproduction • self-defense • metabolism (matter/energy acquisition, growth, repair) • Can be genetically-engineered for our purposes NSF Workshop: Biological Communications Technology

50. The Programmable Microorganism(“Promorg”) • Noncoding DNA can be used for “genetic circuits” • in eukaryotes, 10–70% • equivalent of about 3000 genes in yeast • Equipped with an assortment of generally useful sensors & receptors (especially for self-organization) • Special-purpose modifications for particular applications • Research: principles of design & self-organization NSF Workshop: Biological Communications Technology